Newish restaurants in NY for ex-New Yorker

Fellow hounds, do you have any recs for newer restaurants/food carts/etc that are can't miss spots? I moved out of NY in 2010 so older restaurants are helpful too, but I already have a decent familiarity with the food scene from before 2010 and very little of post 2010. For comparison, some of my favorites then were Ssam Bar, socarrat, Jean Georges, Yasuda, Kanoyama, scarpetta, difara, shake shack, russ and daughters, and Soto.

We will be doing lunch tasting menus at le bern and gramercy tavern so more casual dinner options are most welcome! BK and Flushing are ok.

Hole in the walls, casual neighborhood joints, ethnic food, etc are all great if they are delicious. However, I've been living in LA so probably not burgers, Mexican, Chinese, Korean, or Thai food unless it's phenomenal/unique. Italian and Greek (thinking Kyclades) and pizza (anything comparable to DiFara?) are top choices but any cuisine is good.

For Italian, I was thinking of a Michael White restaurant but would prefer a more casual one (ie not marea) with great pasta. Which would you recommend? Or would a Batali restaurant be better? We do have Mozza in LA.

Thanks in advance! I have about 5 days to stuff myself silly before heading back.